On the Achievable Inertia Constant of Inverter Based Resources

As inverter-based resources (IBRs) displace synchronous generators, the inertia they can actually contribute to the grid becomes a critical planning parameter. Unlike synchronous machines, this contribution is bounded simultaneously by the available energy reserve, the converter power rating combined with voltage ride-through (VRT) obligations, and the inertia-emulation control scheme with its activation delay. This paper derives each bound in closed form and combines them into a unified envelope (t,λ,V g)= (,,), which uses parameters accessible to the system operator to quantify how much inertia a plant can provide at a given loading λ, grid voltage V g, and time t after a disturbance. The analysis shows that below a loading-dependent critical voltage, VRT reactive-current priority does not leave active-current headroom for inertial power injection; that the converter overload ratio κ matters mainly during voltage dips; and that de-loading yields a linear, quantifiable inertia gain, while collocated energy storage (ESS) removes the source-coupling constraint, making grid-following (GFL) and grid-forming (GFM) plants with storage equivalent post-activation, up to the GFL activation-delay discount within short RoCoF measurement windows. Simulations on the IEEE 9-bus system confirm the framework and motivate a two-dimensional inertia capability curve H(λ,V g,) as a grid-code instrument analogous to the P--Q diagram of synchronous generators.